A display apparatus capable of displaying a stereoscopic image (three-dimensional image) is proposed. Furthermore, there is a request to implement two-dimensional image display and three-dimensional image display in the same display apparatus by switching between them, and a technique for satisfying the request is proposed. For example, there is a technique of performing switching between the two-dimensional image display and the three-dimensional image display by using a liquid crystal lens array element. This liquid crystal lens array element has cylindrical electrodes disposed periodically on a first substrate. And electric field distribution is generated between the first substrate and a second substrate which is opposed to the first substrate, and the orientation of the liquid crystal layer is changed by the electric field distribution. As a result, refractive index distribution which acts as a lens is generated. The lens action can be turned on or off by controlling a voltage applied to the electrodes. As a result, switching between the two-dimensional image display and the three-dimensional image display can be conducted. The method for controlling the orientation direction of liquid crystal molecules by the electric field in this way is called liquid crystal gradient index lens method or liquid crystal gradient index (GRIN) lens method.
Furthermore, a technique of applying different voltages of two kinds to the cylindrical electrodes disposed periodically on the first substrate is proposed. And refractive index distribution which is more desirable as the lens array is generated by applying the different voltages of two kinds.
Thus, attempts for implementing the liquid crystal GRIN lens are performed. For implementing favorable three-dimensional image display by using the liquid crystal GRIN lens, however, it is necessary to set the focal length of the liquid crystal GRIN lens nearly equal to a distance between a principal point of the liquid crystal GRIN lens and a pixel plane of an image display unit. For this purpose, refractive power of some degree is required of the liquid crystal layer of the liquid crystal GRIN lens. Since the refractive index anisotropy of liquid crystal molecules are typically as small as approximately 0.2, it is necessary to make the thickness of the liquid crystal layer considerably greater than that of the ordinary display panel. This brings about a problem that not only the cost increases because of an increased use of liquid crystal but also the difficulty in manufacturing increases, too.
Therefore, it is proposed to form the liquid crystal GRIN lens as a Fresnel lens. In the proposal, refractive index distribution serving as a Fresnel lens is implemented by disposing a large number of cylindrical electrodes on a first substrate and applying a large number of different voltages to the cylindrical electrodes.
In a Fresnel lens type liquid crystal GRIN lens array, however, it is necessary to dispose a large number of cylindrical electrodes in each lens and a technique of processing transparent electrodes finely becomes necessary. The fine processing of the transparent electrodes has a problem that the cost increases because a high precision stepper or dry etching apparatus is needed. Furthermore, there is a problem that the cost increases because it is necessary to apply a large number of different voltages to a large number of cylindrical electrodes and the drive becomes complicated.